dlls

import numpy as np
import matplotlib.pylab as plt

def numGrad(f, x):
    h = 1e-4 # 0.0001
    grad = np.zeros_like(x)
    
    for idx in range(x.size):
        tmp_val = x[idx]
        x[idx] = float(tmp_val) + h
        fxhP = f(x) # f(x+h)
        
        x[idx] = tmp_val - h 
        fxhM = f(x) # f(x-h)
        grad[idx] = (fxhP - fxhM) / (2*h)
        
        x[idx] = tmp_val # 値を元に戻す
        
    return grad


def gradDesc(f, init_x, lr=0.01, step_num=100):
    x = init_x
    x_history = []

    for i in range(step_num):
        x_history.append( x.copy() )

        grad = numGrad(f, x)
        x -= lr * grad

    return x, np.array(x_history)


def function_2(x):
    return (x[0]**2)/20 + x[1]**2

init_x = np.array([-3.0, 4.0])    

lr = 0.9
step_num = 100
x, x_history = gradDesc(function_2, init_x, lr=lr, step_num=step_num)

plt.plot( [-5, 5], [0,0], '--b')
plt.plot( [0,0], [-5, 5], '--b')
plt.plot(x_history[:,0], x_history[:,1], '-o')

plt.xlim(-3.5, 3.5)
plt.ylim(-4.5, 4.5)
plt.xlabel("X0")
plt.ylabel("X1")
plt.show()